Of the total number enrolled for so-called "Obamacare," nearly one million signed up in December alone, compared to only 27,000 in October when the website's launched was beset by technical glitches.

The windfall comes at a critical moment for Obama's sweeping health care law, which becomes "real" for many Americans on Jan. 1 when coverage through the exchanges and key patient protections kick in, The Associated Press reported.

The White House last week signaled an extension for sign-ups in light of the last-minute surge and earlier site errors, although it has yet to specify details.

"We are eager to assist millions more Americans gain the health security offered by the Affordable Care Act in the weeks and months ahead," Tavenner added.

Wednesday will bring a fresh test for Obama's flagship policy as hundreds of thousands of Americans will begin to use the program's new medical coverage for the first time, Reuters reported.

For anxious Democrats with an eye on the 2014 congressional elections, it is a chance for the White House to show that its effort to help millions of uninsured and under-insured Americans is finally gaining its footing.

However, there are concerns as to whether the program will work as advertised on January 1, Reuters reported - with some insurance industry executives expressing fear that some people who need medical care during the first days of 2014 will head to the doctor, only to find there is no record of their new insurance.